More than 40% of Scots are already on the NHS Organ Donation Register.
However, new figures, released to encourage more people to make their wishes known to relatives, show 62% of donors had not signed up to give away their organs in the event of their death.
Public Health Minister Michael Matheson said that, although sign-up rates were higher in Scotland than elsewhere in the UK, it was vital families talked about organ donation and made their wishes official.
Among those speaking out as part of the campaign was Jill Polanski, 30, who decided to donate her husband's organs, saving the lives of four people in the process.
Matt Polanski, 30, was killed following an accident at the Knockhill race circuit in Fife just over two months ago. His wife said that deciding to donate his organs was one of the toughest decisions she had made, but it had meant something positive came out of her husband's death.
Mr Polanski's heart saved the life of a woman, his liver went to a man, his kidney and pancreas went to another woman and a teenage boy received a kidney.
Ms Polanski said: "It was one of the hardest things we've ever had to do but I'm so grateful that something positive has come out of Matt's death."
She and her 13-year-old daughter Bethany are now urging other families to talk about organ donation and their wishes.
As part of the campaign adverts will urge people to have a "wee chat" with their loved ones about organ donation.
Mrs Polanski recalled how she and her husband had discussed the issue three years before his death, when he was renewing the photograph on his driving licence.
She had been in the pit lane at Knockhill with Bethany, who was preparing to race that day on August 4, when her husband suffered serious head injuries in the crash.
The motorcyclist was treated by medics at Knockhill before being rushed to Ninewells Hospital in Dundee, but his wife said she knew "that was it" when she saw the condition his helmet was in after the accident.
Mrs Polanski added: "The neurosurgeon then broke the news that the bleeding and trauma to Matt's head was so massive that he'd gone."
She was then asked if she would consider donating his organs.
She recalled: "I remember feeling very numb as the accident had only happened about three hours beforehand. But I knew Matt's wishes and agreed instantly to donate all his organs, apart from his eyes. His family just looked at me but I was able to tell them that I knew that's what he wanted.
"I trained as a dispensing optician and have a medical science background, so I knew how important organ donation was. A close family member of Matt's has one kidney, so my view was very much that if anything happened to that kidney, he would rely on someone else giving one up.
"I clearly remember the discussion and Matt saying he would have no objections for that very reason. He'd made the decision, all I had to do was honour it."
She said their daughter was struggling" to cope.
However, she added: "When I went outside to explain that recipients and their families would be making their way to hospital, Bethany hit me with the grown-up statement that even though her daddy was gone, some other little girl could still have her daddy tomorrow. The way she handled things helped me find peace and cope with those last few difficult hours."
Mrs Polanski said she was planning to write to the people who received her husband's organs "to let them know the comfort it has brought us as a family".
Mr Matheson said: "Matt and Jill's story is a very real example of how important organ donation is and how joining the register could save lives."
BMA Scotland gave its backing to the campaign but said a "soft opt-out" system should be introduced in which people must join a register if they specifically do not want their organs donated.